The vertex of this parabola is at (-3, 6). Which of the following could be its equation? A. y = -3(x + 3)2 + 6
B. y = -3(x + 3)2 - 6
C. y = -3(x - 3)2 + 6
D. y = -3(x - 3)2 - 6
Answers
y=a(x-h)^2+k
(h,k) is vertex
therfor since (-3,6) is vertex
we are looking for something like
y=a(x-(-3))^2+6 simplified to
y=a(x+3)^2+6
A is ansre
The vertex form of a parabola is:
and the vertex is at (h,k).
Thus, the equation will have to look something like this:
Only option A matches these criteria, so is must be the correct option.
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What is the solution set of the following equation 4/5x^2=2x-4/5
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Answers
Answer:
y-intercept = 1/3
Step-by-step explanation:
c = y-intercept
y-intercept= 1/3
Hello! :)
To find the y-intercept, substitute 0 for x-intercept then you will get the y-intercept.
(0,1/3) y-intercept
Hope this helped you!
THEDIPER
(screenshot included)
Answers
Answer:
32÷35=0.9142857142857143
Answer:
decimal equivalent is .91429 (simplified)
he likely made the mistake of dividing 35 by 32 instead of the other way around
Step-by-step explanation:
to find the answer you divide 32 by 35 instead of dividing 35 by 32
Answers
It took 15 gallons to fill those empty 5/8 of a tank.
5/8 x (1 tank) = 15 gallons
1 tank = 15 / (5/8) = 15 x 8/5 =24 gallons
B.Two students have the same height but different ages.
C.No two students are the same age or height.
Answers
Answer:
Option: A is the correct answer.
A. Two students are the same age but have different heights.
Step-by-step explanation:
The height of a student could not be a function of the ages of a student because two or more students with the same age may have the different heights .
This means that a value on a x-axis (i.e. age) is mapped to two or more values i.e. corresponding y-value ( i.e. different heights) which violates the definition of function.
Hence, option: A is the correct answer.
Answers
D. Subtract 4 - 1
Or the distance formula can be used
d = √( (9 - 9)² + (4 - 1)² )
d = √( 0² + 3² )
d = √3²
d = 3
3x –y = 7
Answers
Let's write both equations in the standard form of [ y = mx + b ],
and then see what we can tell about their graphs.
First equation: x + 3y = 9
Subtract 'x' from each side: 3y = -x + 9
Divide each side by 3: y = -1/3 x + 3
This line crosses the y-axis at y=3, and it has a slope of -1/3 .
Second equation: 3x - y = 7
Subtract 3x from each side: -y = -3x + 7
Multiply each side by -1 : y = 3x - 7
This line crosses the y-axis at y=-7, and it has a slope of 3 .
-- The two lines have different slopes, so they're not parallel.
They must intersect somewhere.
-- They're not the same line, so they can't 'intersect' everywhere.
-- They have slopes of -1/3 and 3 . Their slopes are negative reciprocals,
so the lines are perpendicular.
All of this says that the two equations can't have no solution, and they can't have
infinitely many solutions. They must have one and only one solution.
I guess that means that it's our job to find it now.
============================================
For each equation, the "mx + b" form is equal to 'y' . Since these two things are
equal to the same thing, they must be equal to each other, and we can write:
-1/3 x + 3 = 3x - 7
Multiply each side by 3 : -x + 9 = 9x - 21
Add 'x' to each side: 9 = 10x - 21
Add 21 to each side: 30 = 10x
Divide each side by 10 : 3 = x
The intersection/solution is some place where x=3 .
Let's put that back into the first equation:
x + 3y = 9
3 + 3y = 9
Subtract 3 from each side: 3y = 6
Divide each side by 3 : y = 2
And there's your solution: x = 3
y = 2
On the graph, the two lines intersect at the point (3, 2) .
We used the first equation to get part of the solution, so we can't use
the same equation to check the solution. We'll put our solution into the
second equation, and see whether it checks there:
3x - y = 7
3(3) - (2) = 7
9 - 2 = 7
7 = 7 yay !
The two equations have one and only one solution,
and it is definitely x = 3, y = 2 .
Substitution or Elimination
im using substitution
1. solve for variable for one of the equation
x + 3y = 9
x = 9 - 3y
2. Substitute the variable into one of the equation
3 (9-3y) - y = 7
27 - 9y - y = 7
27 - 10y = 7
-10y = 7 - 27
-10y = -20
y = 2
3. sub y = 2 into any equation to find x
3x - 2 = 7
3x = 7 -2
3x = 5
x = 5/3
X+3(2) = 9
x + 6 = 9
x = 9-6
x= 3
therefore there are two solutions x = 3 and x= 5/3